{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:77LKG7H3DCBFITMVCL37DGZW7L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a6d8c0cd1cfbac7ddcd73bf916c64ffed91a85cc230c55061c689c926d1d4f3c","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1996-10-28T10:56:53Z","title_canon_sha256":"769d36855085dc128a699e8bc8f3c62a4ed8f64114b73ed3f1eef24384a5625b"},"schema_version":"1.0","source":{"id":"quant-ph/9610042","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9610042","created_at":"2026-07-04T16:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9610042v2","created_at":"2026-07-04T16:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9610042","created_at":"2026-07-04T16:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"77LKG7H3DCBF","created_at":"2026-07-04T16:02:41Z"},{"alias_kind":"pith_short_16","alias_value":"77LKG7H3DCBFITMV","created_at":"2026-07-04T16:02:41Z"},{"alias_kind":"pith_short_8","alias_value":"77LKG7H3","created_at":"2026-07-04T16:02:41Z"}],"graph_snapshots":[{"event_id":"sha256:e92d5c76e6b32fe82c2eda9aa2353efdf2269018af3856a63a2bcdb19715f107","target":"graph","created_at":"2026-07-04T16:02:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/9610042/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The quantum erasure channel (QEC) is considered. Codes for the QEC have to correct for erasures, i. e., arbitrary errors at known positions. We show that four qubits are necessary and sufficient to encode one qubit and correct one erasure, in contrast to five qubits for unknown positions. Moreover, a family of quantum codes for the QEC, the quantum BCH codes, that can be efficiently decoded is introduced.","authors_text":"(2) Universitaet Innsbruck), Markus Grassl (1), Thomas Beth (1), Thomas Pellizzari (2) ((1) Universitaet Karlsruhe","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1996-10-28T10:56:53Z","title":"Codes for the Quantum Erasure Channel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9610042","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bc11e9c7739af4cc593e09418546266cfa1ef2f410f2fffa75aa69a633283def","target":"record","created_at":"2026-07-04T16:02:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a6d8c0cd1cfbac7ddcd73bf916c64ffed91a85cc230c55061c689c926d1d4f3c","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1996-10-28T10:56:53Z","title_canon_sha256":"769d36855085dc128a699e8bc8f3c62a4ed8f64114b73ed3f1eef24384a5625b"},"schema_version":"1.0","source":{"id":"quant-ph/9610042","kind":"arxiv","version":2}},"canonical_sha256":"ffd6a37cfb1882544d9512f7f19b36facff0274254b96a31ac4c7cdf2bea26c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffd6a37cfb1882544d9512f7f19b36facff0274254b96a31ac4c7cdf2bea26c3","first_computed_at":"2026-07-04T16:02:41.347481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:02:41.347481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c+Nv5GWjh3YCFZuxRRuZhGbMVzAaFuEDju9un/knbVoHoX+EgWgzWRyLODulJr8AGFpNOY6+pp7hfqFQHNnpDA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:02:41.347922Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9610042","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc11e9c7739af4cc593e09418546266cfa1ef2f410f2fffa75aa69a633283def","sha256:e92d5c76e6b32fe82c2eda9aa2353efdf2269018af3856a63a2bcdb19715f107"],"state_sha256":"641910fd940babb4f2eb3e8a599b56038029c4d450644a81b3910d18cb767cca"}